Principle of Mathematical Induction

Principle of Mathematical Induction

Question

Find the value of:

space space space cos open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses

Answer
space space space cos open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses space equals space cos 75 degree space equals space cos left parenthesis 45 degree plus 30 degree right parenthesis space equals space cos 45 degree cos 30 degree minus sin 45 degree sin 30 degree
                  equals fraction numerator 1 over denominator square root of 2 end fraction. space fraction numerator square root of 3 over denominator 2 end fraction minus fraction numerator 1 over denominator square root of 2 end fraction.1 half space equals space fraction numerator 1 over denominator 2 square root of 2 end fraction left parenthesis square root of 3 minus 1 right parenthesis

Hence,      cos open parentheses fraction numerator 5 straight pi over denominator 12 end fraction close parentheses space equals space fraction numerator square root of 3 minus 1 over denominator 2 square root of 2 end fraction

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